Higgs Physics at Hadron Colliders (I)

R. Santos

30 August 2016

ISEL & CFTC (U. Lisboa)

IBS-Honam Focus Program on Particle Physics Phenomenology

The strike

2

a) Many thanks to Shinya for replacing me in the last minute. A beer is due!

Summary of the searches (involving scalars) that are being performed – new particles and new searches?

The simplest extensions of the scalar sector as benchmark models

The singlet extension RxSM and CxSM 2HDMs 3HDMs – Ivanov and Silva’s Half CP

3

a) Disclaimer: this lecture is about scalars and there is no supersymmetry involved

Results for couplings after ICHEP

4

a) no combinations yet

b) with run 1 and run 2 data

The 750 GeV turmoil

5

a)A very interesting and useful exercise for model

builders and phenomenologists!

a) More details - Hyun Min Lee talk

The 750 GeV turmoil

6

a) total results from resonaances.blogspot.pt

a) h-index results from resonaances.blogspot.pt

Higgs production mechanisms

a) Values for the production cross

sections of a SM-like Higgs boson

7

a) Main diagrams for a Higgs with

“reasonable” couplings to fermions

and gauge bosons.

Higgs production mechanisms –new scalars – charged Higgs

a) “main” processes above the top threshold

8

a) “main” process below the top threshold

a) still, cross sections could be negligible

Experimental (LHC)

mt

tanb

mb tanb

Corrected for

ATLAS-CONF-2013-090

I II F LS

tanb 4.3 6.4 3.2 5.2

mH + = 90 GeV

Lauri Wendland talkAT Charged2014

How the ATLAS exclusion plot would look like in types I

and LS (X)

4.3

small tan excluded for this mass region

Deschamps, Descotes-Genon, Monteil, Niess, T’Jampens, Tisserand, 2010

Experimental constraints on the charged Higgs mass vs. tan

Higgs production mechanisms –new scalars – charged Higgs

11

a) Only “model independent” bounds

b) come from lepton colliders

a) bound is roughly half the energy of the collider except if decays are very non-standard

no Yukawa dependence

(except for the decays)

Type LS (X)

Any

Higgs production mechanisms –new scalars – charged Higgs

a) charged Higgs pair production – only interesting when resonant

12

a) similar modes for HW production

Aoki, Guedes, Kanemura, Moretti, RS, Yagyu (2011)

13

“dark”

charged Higgs

Dark scalars production mechanisms

Inert

pp®AH®AVVmost promising but still with

very small cross section (< 2fb)

Fermiophobic

cross sections reach 350 fb (first) and 90 fb (second) at 13 TeV

with BRs close to 100%

Searches involving neutral scalars

CPC

CPV

CP(Hi ) =1; CP(Ai ) = -1

hi (no definite CP)

In run 1 searches were performed inWW, ZZ, ΥΥ and ZΥ.

Searches will continue in run 2. There is some discussion whether ZΥ

is interesting at all at high scalar masses, if there is anythingexperimentalists would be happy to hear.

Analysis are assumed to be independent of particles CP.

CPV

CPC

C2HDM, ...

2HDM, ...

Searches involving neutral scalars

CP(Hi ) =1; CP(Ai ) = -1

hi (no definite CP)

A->Zh125 was done in run 1.A->ZH is done for CMS and is being started in ATLAS.

Analysis are assumed to be independent of particles CP.

Triplets

Searches involving charged scalars

Done by ATLAS

Main decays for CPC and CPV 2HDM are the same.

So far there seems to be no concrete plans even for H+->W+h125

Doubly charged Higgs have been searched for

in leptons and WW.

Si ® S jS j

Si ® S jSk

ì

íï

îï

hi® hjhj

CPC

CPV

Hi ®H jHk

Ai ® A jHk

ì

íï

îï

hi® hjhk

CPC

CPV

NMSSM

CxSM, NMSSM

RxSM, 2HDM, NMSSM

C2HDM,

C-NMSSM

Hi®H jH j (AiAj )

CP(Hi ) =1; CP(Ai ) = -1

hi (no definite CP)

Searches involving neutral scalars

So far only H -> hh.However it covers all cases except final

states with different masses – more later.

Searches involving neutral scalars

Vardan Khachatryan et al. Search for resonant pair production of Higgs bosons decaying totwo bottom quark-antiquark pairs in proton-proton collisions at 8 TeV. Phys. Lett., B749:560–582, 2015.

The ATLAS collaboration. A search for resonant Higgs-pair production in the bbbarbbarbfinal state in pp collisions at √s = 8 TeV. 2014.

G. Aad et al. Search For Higgs Boson Pair Production in the γγbbarb Final State using ppCollision Data at √s = 8 TeV from the ATLAS Detector. Phys.Rev.Lett., 114(8):081802,2015.

CMS Collaboration. Search for the resonant production of two Higgs bosons in the final statewith two photons and two bottom quarks. 2014.

Resonant Si

No charged scalars considered

FC

FCNC

Si (any scalar)

Searches involving scalars

There are also ttH and bbHproduction with H->ttbar

planned as well.

Done

Done and new analysis being prepared

Done for 8 TeV. Being done for run 2.

Being done

Searches involving charged scalars

Done in tt production (mass below the tb threshold)

Done (above the tb threshold)

Done in tt productiona long time ago – no updates.

(mass below the tb threshold)

LHC searches for exotic new particles Tobias Golling, Prog.Part.Nucl.Phys. 90 (2016) 156-200

Other exotic searches that were not covered here can be found in the review

Singlet – RxSM and CxSM

21

a tool for multi-Higgs calculations

23

The singlet

25

a) Provide dark matter candidates

b) Improve stability of the SM at high energies

c) Help explain the baryon asymmetry of the Universe

d) Rich phenomenology with Higgs to Higgs decays

LHC run 2 -> probe extended sectors

Silveira, Zee (i985)

Costa, Morais, Sampaio, Santos (2015)

Profumo, Ramsey-Musolf, Shaughnessy (2007)

CxSM: Phase classification for three possible models

soft breaking terms

27

CxSM: Minimal model with dark mater + 1/2 new Higgs

Barger, Langacker, McCaskey, Ramsey-Musolf, Shaughnessy (2009) and many more...Coimbra, Sampaio, Santos (2013)Costa, Morais, Sampaio, RS (2015)

28

RxSM: Minimal model with dark mater or new Higgs

Datta, Raychaudhuri (1998) Shabinger, Wells (2005) and many more...

29

34

CP and the CxSM

This is a CP-transformation

so, if A gets a vev, CP is broken, right? Wrong!

The model has two phases, one with a dark matter candidate and one where the three neutral scalars mix.

In any case the model is always CP-conserving. The phases only play a role if new particles are added to the theory.

35

CP and the CxSM

Symmetry (2) can be seen as a CP symmetry as long as new fermions are not added to the theory.

Therefore even if (1) is broken there is still one unbroken CP symmetry (2) and the model is CP-conserving.

Transformation (2) ceases to be a CP transformation with e.g. the introduction of vector-like quarks.

The crucial point is the following: V has two CP symmetries

Branco, Lavoura, Silva (1999)

Bento, Branco (1990)

The two phases of CxSM at the LHC

The status of the singlet – scan boxes

Stability conditions under RGE evolution

40

RGE stability bands – no Phenomenology

41

RGE stability + Phenomenology

Lower bound mHnew = 170 GeV from the combination of all imposed constraints. Lower bound on the dark matter particle mass just below mDM = ½ m125 and an excluded wedge around mDM = ½ mHnew

These correspond to regions where the annihilation channels AA → Hi (to visible Higgses) are very efficient in reducingthe relic density so it becomes difficult to saturate the measured Ωc.

2HDMs

42

The 2HDMs

43

a) Also provide dark matter candidates

b) Also improve stability of the SM at high energies

c) Also help to explain the baryon asymmetry of the Universe

d) Also richer phenomenology with Higgs to Higgs decays

e) New types of particles: charged Higgs and pseudo-scalars

f) CP-violation in the scalar sector

All symmetries broken → 4 GB + 4 scalar bosons ( CB)

U(1)em unbroken but not CP → 3 GB + 5 scalar bosons (2 charged, H±, and 3 neutral, h1, h2 and h3)

U(1)em and CP unbroken → 3 GB + 5 scalar bosons (2 charged, H± , and 3 neutral, h, H and A)

All symmetries unbroken → 8 scalar bosons

SM → 4 degrees of freedom

2HDM → 8 degrees of freedom

2HDM particle content

The softly broken Z2 (U(1)) symmetric 2HDM potential

Different models are obtained by tuning m212 and 5 together with the

possible vacuum configurations (all other parameters real – hermiticity)

1 2

1 2

0 ;

' 'v v

1 2

1 2

0 0 ;

' 'vi v

1 2

1 2

0 0 ;

v v

NORMAL (N)

CHARGE BREAKING (CB)

CP BREAKING (CP)

Can one potential have a Normal and a CB minimum simultaneously?

Local minimum –

NORMAL (VN)

Global minimum – CHARGE BREAKING (VCB)

0m

! 0m

CB is possible in 2HDMs! Suppose we live in a 2HDM, are we in DANGER?

Oh No! Not

Charge

Breaking!

2

22

HM

v

Calculated at the Normal stationary point.

VN is a MINIMUM2

20

2

HM

v

N CBV V

The Normal minimum is below the CB SP. The CB SP is a saddle point.

VN is a MINIMUM

For a safer 2HDM

Valid for the most general 2HDM but not for 3HDM!

VCB -VN =M

H ±

2

2v2v'1v2 - v'2 v1( )

2

+ a 2v1

2[ ]

VCB -VN =M

H ±

2

2v2v'1v2 - v'2 v1( )

2

+ a 2v1

2[ ]

VCP -VN =MA

2

2v2v' '1v2 - v' '2 v1( )

2

+d 2v1

2[ ]

For charge breaking

For CP breaking

For 2 competing normal minima

For charge breakingFor charge breaking

Some beautiful relations

Vacuum structure of 2HDMs

The tree-level global picture for spontaneously broken symmetries

1.1. 2HDM have at most two minima

2.2. Minima of different nature never coexist

3. Unlike Normal, CB and CP minima are uniquely determined

4. If a 2HDM has only one normal minimum then this is the absolute minimum – all other SP if they exist are saddle points

5. If a 2HDM has a CP breaking minimum then this is the absolute minimum – all other SP if they exist are saddle points

PLB603(2004), PLB632(2006), PLB652(2007)

PRD75(2007)035001,PRD77(2008)15017,PRE79(2008)021116

I. Ivanov

EPJC48(2006)805

M. Maniatis, A. von Manteuffel, O. Nachtmann and F. Nagel

A. Barroso, P. Ferreira, RSThe tree-level global picture

6. An explicitly CP-violating 2HDM potential can have two non-degenerate minima

7. If they exist they must be non-degenerate

Two normal minima - potential with the soft breaking term

Global minimum (N) –

v = 329 GeV

Local minimum (N) –

v = 246 GeV

VG -VL = - 4.2 ´108 GeV

mW = 80.4 GeV

mW =107.5 GeV

A. Barroso, P.M. Ferreira, I.P. Ivanov, RS, JHEP06 (2013) 045.

A. Barroso, P.M. Ferreira, I.P. Ivanov, RS, J.P. Silva, Eur. Phys. J. C73 (2013) 2537.

THE PANIC VACUUM!

and this is one that can actually occur...

However, two CP-conserving minima can coexist – we can force the potential to be in the global one by using a simple condition.

2HDMs are stable at tree-level – once you are in a CP-conserving minimum,charge breaking and CP-breaking stationary points are saddle point above it.

Our vacuum is the global minimum of the potential if and only if D > 0.

Barroso, Ferreira, RS (2006)

Barroso, Ferreira, Ivanov, RS (2012)

D =m12

2 m11

2 - k2m22

2( ) tanb - k( )

k =l1

l2

æ

è ç

ö

ø ÷

1/ 4

2HDMs Higgs Potential and the vacuum

52

In the case of explicit CP-breaking 2HDMs two minima can also coexist. In that case the condition is:

Ivanov, Silva (2015)

Softly broken Z2 symmetric Higgs potential

we choose a vacuum configuration

F1 =1

2

0

v1

æ

è

çç

ö

ø

÷÷; F2 =

1

2

0

v2

æ

è

çç

ö

ø

÷÷

V (F1, F2 ) =m1

2F1

+F1 +m2

2F2

+F2 - m12

2 F1

+F2 + h.c.( ) +l1

2F1

+F1( )2

+l2

2F2

+F2( )2

+ l3 F1

+F1( ) F2

+F2( ) + l4 F1

+F2( ) F2

+F1( ) +l5

2F1

+F2( )2

+ h.c.éëê

ùûú

m212 and 5 real potential is CP-conserving (2HDM)

m212 and 5 complex potential is explicitly CP-violating (C2HDM)

53Ginzburg, Krawczyk, Osland (2002).

Parameters

ratio of vacuum expectation values

tanb =v2

v1

2 charged, H±, and 3 neutral

rotation angles in the neutral sector

CP-conserving - h, H and A

CP-violating - h1, h2 and h3

CP-conserving – α

CP-violating - α1, α2 and α3

soft breaking parameter

CP-conserving – m212

CP-violating – Re(m212) 54

Lightest Higgs couplings

to gauge bosons

g2HDM

hVV = sin(b -a) gSMhVV V =W,Z

gC2HDM

hVV =C gSMhVV = (cbR11 + sbR12 ) gSM

hVV = cos(a2 )cos(b -a1) gSMhVV

a1 =a +p / 2

C º cbR11 + sbR12

gC2HDM

hVV = cos(a2 ) g2HDM

hVV

R =

c1c2 s1c2 s2

-(c1s2s3 + s1c3) c1c3 - s1s2s3 c2s3

-c1s2c3 + s1s3 -(c1s3 + s1s22c3) c2s3

æ

è

çççç

ö

ø

÷÷÷÷

kVh = sin(b - a)

kVH = cos(b - a)

55

YdR uReRL L LLUDY DUD YUE YEh.c.

where the gauge eigenstates are

ggggggeUuct; Ddsb; N; Ee

and Y are matrices in flavour space. To get the mass terms we just need the vacuum expectation values of the scalar fields

mass

Y LuR LdR LeR

v v vL UYU DYD EYEh.c.2 2 2

which have to be diagonalised.

SM Yukawa Lagrangian

So we define

1 1 1 1

RRRLLLRRRLLLDND;DND;UKU;UKU

and the mass matrices are

냶LdRd LuRu

v v NYNM; KYKM2 2

and the interaction term is proportional to the mass term (just D terms)

interactions

Y LdR LdR

h vL DYD DYD

2 2

No scalar induced tree-level FCNCs

SM Yukawa Lagrangian

? 2 ? 2

L1d2dRd L1u2uRu

1 1 NvYvYNM; KvYvYKM2 2

1 2

11 22

; (hv)/2 (hv)/2

mass 1 1 2 21 1 2 2Y LuR LdR LuR LdR

1 2 1 2

L1u 2uR L1d 2dR

v v v vL UYU DYD UYU DYD...

2 2 2 2

1 1 UvYvYU DvYvYD...

2 2

However in 2HDMs

interactions 1 1 2 21 1 2 2Y LuR LdR LuR LdR

1 2 1 2

L u uR L d dR

h h h hL UYU DYD UYU DYD...

2 2 2 2

h H UcosYsinYU DsinYcosYD...

2 2

h, H are the mass eigenstates (α is the rotation angle in the CP-even sector)

2HDM Yukawa Lagrangian

How can we avoid large tree-level FCNCs?

1. Fine tuning – for some reason the parameters that give rise to tree-level FCNC are small

Example: Type III models

2. Flavour alignment – for some reason we are able to diagonalisesimultaneously both the mass term and the interaction term

Example: Aligned models

Yd

2 µ Yd

1 (for down type)

Pich, Tuzon (2009)

Cheng, Sher (1987)

2HDM Yukawa Lagrangian

RRRRRRDD;EE;UU

3. Use symmetries– for some reason the L is invariant under some symmetry

i i i

Y idR iuR ieRL L Li

LUDY DUD YUE YEh.c.

1 12 2;

I 2 2 2

Y2dR2uR2eRL L LLUDY DUD YUE YEh.c.

2HDM Yukawa Lagrangian

3.1 Naturally small tree-level FCNCs

Example: BGL Models

3.2 No tree-level FCNCs

Example: Type I 2HDM Z2 symmetries

Branco, Grimus, Lavoura (2009)

Glashow, Weinberg; Paschos (1977)

Barger, Hewett, Phillips (1990)

Yukawa couplings

a1 =a +p / 2Lightest Higgs couplings

kUI = kD

I = kLI =

cosa

sinbType I

Type II

kUII =

cosa

sinb

kDII = kL

II = -sina

cosb

Type F/Y

Type LS/X

kUF = kL

F =cosa

sinb

kULS = kD

LS =cosa

sinb

kLLS = -

sina

cosb

kDF = -

sina

cosb

c2 = cos(a2 )

tb = tanb

61

YC2HDM º c2Y2HDM ± ig5s2

tb

1/ tb

ì

íï

îï

º aF + ig5bF

Status of the CP-conserving 2HDM

62

All models

Experimental

Theoretical

Vacuum Stability

Perturbative Unitarity

Global minimum (discriminant)

Precision Electroweak

• Set mh = 125 GeV.

• Generate random values for potential’s parameters such that

• Impose all experimental and theoretical constraints previously described.

• Calculate all branching ratios and production rates at the LHC.

Scan (light scenario)

• Impose ATLAS and CMS results.

125 GeV =mh £mH £ 900 GeV

• Set mH = 125 GeV.

• Generate random values for potential’s parameters such that

• Impose all experimental and theoretical constraints previously described.

• Calculate all branching ratios and production rates at the LHC.

Scan (heavy scenario)

• Impose ATLAS and CMS results.

mh £mH =125 GeV

Alignment and wrong-sign Yukawa

Wrong-sign Yukawa coupling – at least one of the couplings of h to down-type and up-type fermion pairs is opposite in sign to the corresponding coupling of

h to VV (in contrast with SM).

sin(b -a) =1 Þ kD =1; kU =1; kW =1

kDkW < 0 or kUkW < 0

The Alignment (SM-like) limit – all tree-level couplings to fermions and gauge bosons are the SM ones.

The actual sign of each κi depends on the chosen range for the angles.

sin(β + α) = 1

sin(β - α) = 1

The SM-like limit (alignment)

kF =1; kV =1

sin(b -a) =1 Þ

Wrong-sign limit

kDkV < 0 or kUkV < 0

Results after run 1 for the CP-conserving case

at tree-level

k i =g2HDM

gSM

OLD PLOT – just to show the behaviour

with sin

Wrong-sign limit (type II and F)

sin(b+ a) =1 Þ kD = -1 (kU =1)

sin(b - a) =tan2 b -1

tan2 b +1 Þ kV ³ 0 if tanb ³1

1509.00672

Ferreira, Gunion, Haber, RS (2014).

Ferreira, Guedes, Sampaio, RS (2014).

68

kDkV < 0 or kUkV < 0

Ginzburg, Krawczyk, Osland 2001

cos(β + α) = 1

cos(β - α) = 1The Alignment limit

Þ kF = -1; kV = -1

cos(b -a) =1 Þ

cos(b+a) =1 Þ kD =1 (kU = -1)

cos(b - a) = -tan2 b -1

tan2 b +1 Þ kV £ 0 if tanb ³1

Wrong-sign limit

kDkV < 0

The heavy scenario (mh < mH = 125 GeV)

69

but no decouupling

Difference decreases with tan

Why is it not excluded yet?

SM-like limit Wrong sign

kD = - sina

cosb = -1+e

Defining

sin(b + a) - sin(b - a) = 2(1-e)

1+tan2b << 1

(tanb >>1)

Probing Wrong-sign limit and SM-like limit in Heavy Scenario

1.5% accuracy in the measurement of the gamma gamma rate

2.could probe the wrong sign in both scenarios but also the SM-like limit in the heavy scenario due to the effect of charged Higgs loops + theoretical and

experimental constraints.

Ferreira, Guedes, Sampaio, RS (2014).

1.Because mh < mH (by construction), if mH = 125 GeV, mh is light and there is no decoupling limit.

71

gHH +H -

SM -like » -2m

H ±

2 -mH

2 - 2M 2

v 2

Boundness from below

1.SM-like

2.(Heavy Scenario)

M < mH

2 +mh2 /tan2 b

b -> s γ

mH±

2 > 340 GeV (® 500 GeV)

gHH +H -

Wrong Sign » -2m

H ±

2 -mH

2

v 2

1.Wrong Sign

2.(Both Scenarios)

Updated in Misiak eal (2015). 72

How come we have no points at 5 %?

Considering only gauge bosons and fermion loops we should find points

at 5 % for the wrong-sign scenario.

In fact, if the charged Higgs

loops were absent, changing the sign

of κD would imply a change in κγ of less

than 1 %.

The relative negative values (and almost constant) contribution from the charged Higgs loops forces the wrong sign μγγ to be below 1.

It is an indirect effect.

1.The two scenarios (distinguished by the sign of sin ) can be distinguished in all models but sometimes very precise measurements are needed

Heavy scenario for type I

Status of a CP-violating 2HDM –the C2HDM

74

Fontes, Romão, Silva (2014)Fontes, Romão, RS, Silva (2015)

• Set mh1 = 125 GeV.

• Generate random values for potential’s parameters such that,

Scan

• Impose pre-LHC experimental constraints,

• Impose theoretical constraints: perturbative unitarity, potential bounded from below.

Results after run 1

α1 vs. α2

for Type I and Type II. The rates are taken to be within 20% of the SM predictions. The colours are superimposed; cyan for μVV, blue for μττ and red for

μγγ.

Results after run 1

tanβ as a function of R11, R12 and R13 for Type I

and Type II. Same colour code.

• There is only one way to make the pseudoscalar component to vanish

The zero scalar scenarios

R13 = 0 Þ s2 = 0

c2 = 0 Þ gh1VV = 0

and they all vanish (for all types and all fermions).

R11 = 0 Þ c1c2 = 0

• There are two ways of making the scalar component to vanish

R12 = 0 Þ s1c2 = 0

excluded

excluded

c1 = 0 allowed

• So, taking

The zero scalar scenarios

c1 = 0 Þ R11 = 0

andaU

2 =c2

2

sb

2; bU

2 =s2

2

tb2

; C2 = sb

2c2

2

Type I

Type II aD = aL = 0

Type F

Type LS

aU = aD = aL =c2

sb

bU = -bD = -bL = -s2

tb

aD = 0

aL = 0

bD = bL = -s2tb

bD = -s2tb

bL = -s2tb

Even if the CP-violating parameter is small, large

tanβ can lead to large values of b.

In Type II, if

The zero scalar scenarios

aD = aL » 0 Þ bD = bL »1

and the remaining h1 couplings to up-type quarks and gauge bosons are

aU2 = (1- s2

4 ) = (1-1/ tb4 )

bU2 = s2

4 =1/ tb4

ì

íï

îï

gC2HDM

hVV

gSMhVV

æ

èç

ö

ø÷

2

= C2 =tb

2 -1

tb2 +1

=1- s2

2

1+ s2

2

This means that the h1 couplings to up-type quarks and to gauge bosons have to be very close to the SM Higgs ones.

tanβ as a function of sin(α1 – π/2) for Type I, Type II and LS. Full range (cyan), s2 < 0.1 (blue) and s2 < 0.05 (red).

Results after run 1

SM-like limit sin(β - α) = 1 sin(β + α) = 1

No major differences relative to the CP-conserving

case

Scalar or pseudo-scalar?

YC2HDM º aF + ig5bF

bU = 0 and aD = 0?

It's CP-violation!

Find a 750 GeV scalar decaying to tops

Find a 750 GeV pseudoscalar decaying to taus

h1 =H® tt

h1 = A®t +t -

Type II

Left: sgn(C) bD (or bL) as a function of sgn(C) aD (or aL) for Type II, 13 TeV, withrates at 10% (blue), 5% (red) and 1% (cyan) of the SM prediction.

Right: same but for up-type quarks.

The CP-

conserving line

limit

sin(α2) = 0

The SM-like

limit

sin(β - α) = 1

The wrong-sign

limit

sin(β + α) = 1 The

pseudoscalar

limit scenario.

So what about EDMs?

Direct probing at the LHC (ττh)

pp®h®t +t -

tanft =bL

aLNumbers from:

Berge, Bernreuther, Kirchner, EPJC74, (2014) 11, 3164.

Berge, Bernreuther, Ziethe 2008Berge, Bernreuther, Niepelt, Spiesberger, 2011Berge, Bernreuther, Kirchner 2014

Dft = 40º 150 fb-1

Dft = 25º 500 fb-1

ì

íï

îï

A measurement of the angle

can be performed with the accuracies

tanft = -sb

c1

tana2 Þ tana2 = -c1

sb

tanft

It is not a measurement of the CP-violating angle α2.

More later!

CP-violation with a combination of three decays

Combinations of three decays

h3®h2h1 Þ CP(h3) = CP(h2 ) CP(h1) = CP(h2 )

h2(3) ®h1Z CP(h2(3)) = -1

Decay CP eigenstates Model

None C2HDM, other CPV extensions

2 CP-odd; None C2HDM, NMSSM,3HDM...

3 CP-even; None C2HDM, cxSM, NMSSM,3HDM...

h1® ZZ Ü CP(h1) =1

h2 ® ZZ CP(h2 ) =1

h3®h2Z CP(h3) = - CP(h2 )

Already observed

Classes of CP-violating processes

Fontes, Romão, RS, Silva (2015).

In 2HDMs

only

Classes involving scalar to two scalars decays

only two to go

on going searches

87

Observing the three decays constitutes a "model

independent" sign of CP-violation.

α2 is already constrained by the first decay. The constraints from

the other two decays could be combined in a (m2, sinα2) plane.

CP-violating class C2 (and C3 and C4)

h1® ZZ Ü CP(h1) =1

h2 ® ZZ Ü CP(h2 ) =1

h2 ®h1Z Þ CP(h1)¹CP(h2 )

c =BR(h2 ® ZZ)

BR(h2 ® h1Z)

The benchmark plane is (m2, χ)

h2 ® h3 h1® h2

88

h1® ZZ Ü CP(h1) =1

Class C7

h3®h1Z Þ CP(h3) = - CP(h1) = -1

h3®h1h1 Ü CP(h3) =1

89

a special 3HDM

90

91

Slides by I. Ivanov

92

Slides by I. Ivanov

93

Slides by I. Ivanov

94

Slides by I. Ivanov

I. P. Ivanov and J. P. Silva, PRD 93, 095014 2016

95

END of Part I